# ON ENTIRE RATIONAL MAPS OF REAL SURFACES

• Ozan, Yildiray
• Published : 2002.01.01
• 59 4

#### Abstract

In this paper, we define for a component $X_{0}$ of a nonsingular compact real algebraic surface X the complex genus of $X_{0}$, denoted by gc($X_{0}$), and use this to prove the nonexistence of nonzero degree entire rational maps f : $X_{0}$ Y provided that gc(Y) > gc($X_{0}$), analogously to the topological category. We construct connected real surfaces of arbitrary topological genus with zero complex genus.

#### Keywords

real algebraic surfaces;algebraic homology;entire rational maps

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